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Consider A=[(4,1),(5,3)]. Verify (A^T)^-...

Consider `A=[(4,1),(5,3)]`. Verify `(A^T)^-1=(A^-1)^T`.

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BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. Let A=[(-1,2,4),(1,1,3),(3,2,3)] Verify that A. AdjA=|A|.I

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  2. Consider A=[(4,1),(5,3)]. Find A^-1 and A^T

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  3. Consider A=[(4,1),(5,3)]. Verify (A^T)^-1=(A^-1)^T.

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  4. Let A=[(1,4,0),(-1,2,2),(0,0,2)] Is A singular?

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  5. Let A=[(1,4,0),(-1,2,2),(0,0,2)] Find Adj A.

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  6. Let A=[(1,4,0),(-1,2,2),(0,0,2)] Find A^-1

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  7. Evaluate |[x, y, x+y],[ y, x+y, x],[ x+y, x, y]|

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  8. Let A = [[1,Sintheta,1],[-Sintheta,1,Sintheta],[-1,-Sintheta,1]], wher...

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  9. Consider the system of equations x-y+z=3,2x+y-z=2,-x-2y+2z=1. Convert ...

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  10. Consider the system of equations x-y+z=3,2x+y-z=2,-x-2y+2z=1. Is A inv...

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  11. Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Express thi...

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  12. Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Prove that ...

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  13. Ashok purchased 3 pencils, 2 instrument boxes and 1 pen and paid Rs 41...

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  14. Ashok purchased 3 pencils, 2 instrument boxes and 1 pen and paid Rs 41...

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  15. If A=[(1,2,-3),(2,3,2),(3,-3,-4)] Is A non-singular? Why?

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  16. If A=[(1,2,-3),(2,3,2),(3,-3,-4)] find A^-1.

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  17. If A=[(1,2,-3),(2,3,2),(3,-3,-4)] Solve the system of linear equations...

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  18. If A^(-1)=[[3,-1,1],[-15,6,-5],[5,-2,2]] and B=[[1,2,-2],[-1,3,0],[0,-...

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  19. Ifabs[[1,-3,2],[4,-1,2],[3,5,2]]=40,thenabs[[1,4,3],[-3,-1,5],[2,2,2]]...

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  20. Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

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